What position in the distribution is suitably "scientifically rigorous"? Should all children's cartoons represent only the population mean? Or perhaps the media

What position in the distribution is suitably "scientifically rigorous"? Should all children's cartoons represent only the population mean? Or perhaps the median - at least that is guaranteed to actually exist. Maybe the mode would be better - but what if there is more than one? We could be willing to be a bit more relaxed, and allow anything within the middle two quartiles. Or, perhaps, we should just remember that there is a distinction between material produced for children and the academic consensus.